Latent class distributional regression for the estimation of non-linear reference limits from contaminated data sources

Abstract

Background Medical decision making based on quantitative test results depends on reliable reference intervals, which represent the range of physiological test results in a healthy population. Current methods for the estimation of reference limits focus either on modelling the age-dependent dynamics of different analytes directly in a prospective setting or the extraction of independent distributions from contaminated data sources, e.g. data with latent heterogeneity due to unlabeled pathologic cases. In this article, we propose a new method to estimate indirect reference limits with non-linear dependencies on covariates from contaminated datasets by combining the framework of mixture models and distributional regression. Results Simulation results based on mixtures of Gaussian and gamma distributions suggest accurate approximation of the true quantiles that improves with increasing sample size and decreasing overlap between the mixture components. Due to the high flexibility of the framework, initialization of the algorithm requires careful considerations regarding appropriate starting weights. Estimated quantiles from the extracted distribution of healthy hemoglobin concentration in boys and girls provide clinically useful pediatric reference limits similar to solutions obtained using different approaches which require more samples and are computationally more expensive. Conclusions Latent class distributional regression models represent the first method to estimate indirect non-linear reference limits from a single model fit, but the general scope of applications can be extended to other scenarios with latent heterogeneity.

Mixture density networks for the indirect estimation of reference intervals

“…For this purpose, a common strategy is the use of expectation-maximization (EM) [17]. The framework is also applicable in latent class regression settings [27] and has further already been evaluated in the context of reference interval estimation [15]. However, EM-algorithms usually estimate the mixture weights independent from covariates, i.e.…”

“…The implemented EM-algorithm is basically identical to the approach described in Hepp et al [15] (also provided in the Additional files) and can be considered as the current benchmark for conditional mixture modeling in the field of reference interval estimation. The model parameters of the mixture components are estimated via the maximum likelihood approach implemented in the gamlss-package for generalized additive models for location scale and shape [36].…”

“…[13,14]). To overcome this limitation, we suggested the use of conditional finite mixture models in the form of latent class distributional regression [15] by relying on generalized additive models for location scale and shape (GAMLSS) [16] to represent the latent mixture components in an expectation-maximization (EM) framework [17]. The suggested model provides an integrated approach that requires only a single fit to the data in order to account for both non-linear effects of covariates on multiple distribution parameters and unlabeled health status.…”

Mixture Density Networks for the Indirect Estimation of Reference Intervals

“…In order to investigate and compare the different approaches we first adopted the simulation study used in Hepp et al [15] as baseline setting. However, since a key difference between the applied algorithms is their ability to account for the effects of covariates on the component weights, we extended the setting to highlight the performance in scenarios where the proportions of the components in fact vary for different values of a covariate.…”

“…The implemented EM-algorithm is basically identical to the approach described in Hepp et al [15] (also provided in the Supplements) and can be considered as the current benchmark for conditional mixture modeling in the field of reference interval estimation. The model parameters of the mixture components are estimated via the maximum likelihood approach implemented in the gamlss-package for generalized additive models for location scale and shape [36].…”